Is there a way to calculate SE for the factor scores from the EFA output? We are able to calculate the factor scores themselves, and we are trying to avoid re-running a number of EFA models in CFA format.

Thank you - I actually am not fully aware what I should do to best take advantage of the factor score standard errors. I guess I could construct confidence intervals and see how the factor scores differ from each other at different levels?

Re focusing on factor scores, it's mainly for specific modelling situations, for example, in ESEM, sometimes the factor structure can change depending on covariate - even the covariate is not part of the model.

Another reason to use factor scores is for colleagues who do not want to go into latent variable but still want to take advantage of psycho-metrically defined variables. But apart from problems of computing factor scores itself, I found in settings such as the bi-factor CFA, the 0 correlations between factors are ignored in factor scores. Although I have not tried Bayes yet, but the idea of plausible values sound much better in general.

I also have some questions about factor score standard errors and their availability in Mplus 7.2

Could you please summarize the cases where SEs are (or are not) available for TYPE = GENERAL analyzes? e.g, for which types of indicators variables (e.g., continuous, categorical, tobit, combinations thereof)? Does this depend on the estimator used?

Also, I believe that Mplus uses "modal a' posteriori" estimates for cases in which factor scores are available (equation 231 in the technical appendices). For Gaussian indicators, this coincides with the posterior mean of the factors, so the standard errors are available from the posterior covariance matrix. For non-continuous indictors, how are the SEs obtained for the MAP estimator? A reference here would be great.